A general methodology for fast online changepoint detection

We propose a general methodology for online changepoint detection which allows the user to apply offline changepoint tests on sequentially observed data. The methodology is designed to have low update and storage costs by testing for a changepoint over a dynamically updating grid of candidate changepoint locations backward in time. For a certain class of test statistics the methodology is guaranteed to have update and storage costs scaling logarithmically with the sample size. Among the special cases we consider are changes in the mean and the covariance of multivariate data, for which we prove near-optimal and non-asymptotic upper bounds on the detection delays. The effectiveness of the methodology is confirmed via a simulation study, where we compare its ability to detect a change in the mean with that of state-of-the-art methods. To illustrate the applicability of the methodology, we use it to detect structural changes in currency exchange rates in real-time.